Unified coordinate system for multiple CT scans of patient lungs

ABSTRACT

A CT alignment system includes a central processing unit (CPU) that processes a plurality of CT images. The CPU determines a location of a main carina from the plurality of CT images and sets the main carina as a point of origin. An x-coordinate, a y-coordinate, and a z-coordinate is calculated for each pixel in each CT image among the plurality of CT images based on the point of origin. A 3D model is rendered from the plurality of CT images and the x-coordinate, the y-coordinate, and the z-coordinate for each pixel in each CT image is associated with a corresponding voxel in the 3D model. The x-coordinate, the y-coordinate, and the z-coordinate for each corresponding voxel in the 3D model is stored as voxel position data. A graphics processing unit (GPU) renders a three dimensional (3D) model based on the plurality of CT images and the voxel position data which is displayed on a display.

CROSS-REFERENCE TO RELATED APPLICATIONS

This application is a continuation of U.S. patent application Ser. No.15/665,514 filed on Aug. 1, 2017, which is a continuation of U.S. patentapplication Ser. No. 14/788,952 filed on Jul. 1, 2015, which claims thebenefit of, and priority to, U.S. Provisional Patent Application No.62/020,242, filed on Jul. 2, 2014, the entire contents of which areincorporated herein by reference.

BACKGROUND 1. Technical Field

The present disclosure relates to systems and methods for processingcomputed tomography (CT) images to align multiple sets of CT images in aunified coordinate system.

2. Discussion of Related Art

Visualization techniques related to visualizing a patient's lungs havebeen developed so as to help clinicians perform diagnoses and/orsurgeries on the patient's lungs. Visualization is especially importantfor identifying a location of a diseased region. Further, when treatingthe diseased region, additional emphasis is given to identification ofthe particular location of the diseased region so that a surgicaloperation is performed at the correct location.

In the past, scanned two-dimensional (2-D) images of the lungs have beenused to aid in visualization. In order to obtain the scanned 2-D images,a patient undergoes multiple CT scans. However, each CT scan has adifferent coordinate system based on scan parameters, start point(s),and field of view. When specifying a location in the lung, a user wouldspecify a slice number along the Z-axis and then a pixel coordinate intwo dimensions of the image starting from the top left corner of theimage left to right on an X-axis and top to bottom on a Y-axis). TheDigital Imaging and Communications in Medicine (DICOM) standard hascoordinate conventions that define the patient orientation in the imagewhich are included in the specific scan and/or machine.

SUMMARY

A system for aligning CT images in accordance with the presentdisclosure includes a central processing unit (CPU) that processes aplurality of CT image sets. The CPU processes each CT image set bydetermining a location of a main carina from a plurality of CT images inthe CT image set, setting the main carina as a point of origin,calculating an x-coordinate, a y-coordinate, and a z-coordinate for eachpixel in each CT image among the plurality of CT images based on thepoint of origin, rendering a 3D model from the plurality of CT images,associating the x-coordinate, y-coordinate, and z-coordinate for eachpixel with a corresponding voxel in the 3D model, and storingx-coordinate, y-coordinate, and z-coordinate for each correspondingvoxel in the 3D model as voxel position data. The system also includes agraphics processing unit (GPU) that processes the 3D model for each ofthe CT image sets in the plurality of CT image sets based on the voxelposition data and a display that displays a first 3D model and a second3D model.

In aspects, the CPU determines a first CT image among the plurality ofCT images, wherein the first CT image includes the main carina, sets thez-coordinate for each pixel in the first CT image as zero, determinesthe x-coordinate for each pixel in the first CT image based on the pointof origin, determines the y-coordinate for each pixel in the first CTimage based on the point of origin, and stores the z-coordinate, thedetermined x-coordinate, and the determined y-coordinate for each pixelin the first CT image as first pixel position data.

In another aspect, the CPU processes a second CT image among theplurality of CT images, determines a z-coordinate for each pixel in thesecond CT image based on a distance between the first CT image and thesecond CT image, sets a reference point in the second CT image, whereinthe reference point is axially aligned along a z-axis with the point oforigin, determines the x-coordinate for each pixel in the second CTimage based on the reference point; determines the y-coordinate for eachpixel in the second CT image based on the reference point, and storesthe determined z-coordinate, the determined x-coordinate, and thedetermined y-coordinate for each pixel in the second CT image as secondpixel position data.

In some aspects, the plurality of CT images are obtained from a datastore.

In other aspects, the display displays the first 3D model and the second3D model side by side. Further, the first 3D model and the second 3Dmodel are synchronized thereby permitting a user to manipulate the first3D model and the second 3D model simultaneously.

The present disclosure also provides another system for aligning CTimages that includes a CPU that processes a plurality of CT image sets.The CPU processes each CT image set by determining a location of a maincarina, a right lobe carina, and a left lobe carina from a plurality ofCT images in the CT image set, setting a reference plane based on thelocation of the main carina, the right lobe carina, and the left lobecarina, setting the main carina as a point of origin, calculating anx-coordinate, a y-coordinate, and a z-coordinate for each pixel in eachCT image among the plurality of CT images based on the point of originand the reference plane, and rendering a 3D model from the plurality ofCT images, associating the x-coordinate, the y-coordinate, and thez-coordinate for each pixel in each CT image with a corresponding voxelin the 3D model, storing the x-coordinate, the y-coordinate, and thez-coordinate for each corresponding voxel in the 3D model as voxelposition data. The system also includes a GPU that processes the 3Dmodel for each of the CT image sets in the plurality of CT image setsbased on the voxel position data and a display that displays a first 3Dmodel and a second 3D model.

In some aspects, the CPU processes a CT image among the plurality of CTimages, determines a z-coordinate for each pixel in the CT image basedon a distance from the point of origin, sets a reference point in the CTimage, wherein the reference point is coplanar with the reference planeand axially aligned along a z-axis with the point of origin, determinesthe x-coordinate for each pixel in the second CT image based on thereference point; determines the y-coordinate for each pixel in thesecond CT image based on the reference point, and stores the determinedz-coordinate, the determined x-coordinate, and the determinedy-coordinate for each pixel in the CT image the pixel position data.

In some aspects, the plurality of CT images are obtained from a datastore.

In other aspects, the display displays the first 3D model and the second3D model side by side. Further, the first 3D model and the second 3Dmodel are synchronized thereby permitting a user to manipulate the first3D model and the second 3D model simultaneously.

Any of the above aspects and embodiments of the present disclosure maybe combined without departing from the scope of the present disclosure.

BRIEF DESCRIPTION OF THE DRAWINGS

Various aspects and features of the present disclosure are describedhereinbelow with references to the drawings, wherein:

FIG. 1 is a schematic representation of a system for aligning multipleCT images in accordance with aspects of the present disclosure;

FIG. 2 is a perspective view of a patient illustrating a method used toalign the CT images in accordance with aspects of the presentdisclosure;

FIG. 3 is a perspective view of a patient illustrating another methodused to align the CT images in accordance with another aspect of thepresent disclosure; and

FIG. 4 is a side by side view of two CT scans that are aligned inaccordance with the aspects of the present disclosure.

DETAILED DESCRIPTION

The present disclosure is related to devices, systems, and methods foraligning multiple sets of CT images in a unified coordinate system.Alignment of multiple sets of CT images may be a necessary component ofpathway planning for performing an ELECTROMAGNETIC NAVIGATIONBRONCHOSCOPY® (ENB) procedure using an electromagnetic navigation (EMN)system as well as monitoring the progression and/or regression of tumorsor lesions.

An ENB procedure generally involves at least two phases: (1) planning apathway to a target located within, or adjacent to, the patient's lungs;and (2) navigating a probe to the target along the planned pathway.These phases are generally referred to as (1) “planning” and (2)“navigation.” The planning phase of an ENB procedure is more fullydescribed in commonly-owned U.S. patent application Ser. Nos.13/838,805; 13/838,997; and Ser. No. 13/839,224, all entitled “PathwayPlanning System and Method,” filed on Mar. 15, 2013, by Baker, theentire contents of which are hereby incorporated by reference. Thepatient's lungs are imaged by, for example, a computed tomography (CT)scan, although additional applicable methods of imaging will be known tothose skilled in the art. The images may be taken prior to planning,prior to navigation, and/or after treatment. The image data assembledduring the CT scans may then be stored in, for example, the DigitalImaging and Communications in Medicine (DICOM) format, althoughadditional applicable formats will be known to those skilled in the art.The CT scan image data may then be loaded into a planning softwareapplication (“application”) to be used during the planning phase of theENB procedure.

Embodiments of the CT alignment systems and methods are described withreference to the accompanying drawings. Like reference numerals mayrefer to similar or identical elements throughout the description of thefigures. As shown in the drawings and as used in this description, the“positive X direction” is from the patient left lateral to the rightlateral, the “positive Y direction” is from the patient's anterior tothe posterior, and the “positive Z direction” is from the patient'sinferior to the superior.

This description may use the phrases “in an embodiment,” “inembodiments,” “in some embodiments,” or “in other embodiments,” whichmay each refer to one or more of the same or different embodiments inaccordance with the present disclosure.

With reference to FIG. 1, a CT alignment system 100 is provided inaccordance with an embodiment of the present disclosure. The CTalignment system 100 aligns the CT scan image data to a right handorthogonal coordinate system that is tied to a major anatomical landmarkwithin the patient's body thereby removing ambiguity when referring tolocations between CT scans taken at different times and/or withdifferent equipment. The CT alignment system 100 enables reviewing andcomparing more than one CT scan of a patient with very easy manipulationof the data while enabling an easy method to communicate locations inthe anatomy, e.g., the lung, that are not related to a specific machineor to detailed labeling of the anatomy.

As shown in FIG. 1, CT alignment system 100 receives CT scan image datafrom a data source 102. Data source 102 may be a server having CT scanimage data obtained during pre-surgical testing stored thereon or datasource 102 may be a device capable of obtaining CT images in real-time.System 100 also includes a central processing unit (CPU) 104, a memory106, a network interface card (NIC) 108 and a graphics processing unit(GPU) 110. A workstation 111 includes a display 112 and input device 114that allows a user to view the CT scan image data as well as manipulatethe CT scan image data.

FIG. 2, which will be described while making reference to FIG. 1,depicts one method of aligning the CT scan image data using a referencepoint in the body of the patient using the system 100. As shown in FIG.2 the point of origin 116 is located at the midst of the main carina118. During a CT scanning procedure individual CT scan slices 120 ₁, 120₂ . . . 120 _(n) are taken along the Z-axis and stored in data source102. The CT scan slices 120 are provided to the CPU 104 which uses analgorithm stored in memory 106 to determine the x, y, z coordinates ofone or more pixels in one or more of the CT scan slices. Because the CTscan slices are parallel to the XY-plane, the z-coordinate for each CTscan slice is equal to the distance between the CT scan slice 120 n,which includes the point of origin 116, and the particular CT scanslice. Each pixel within the particular CT scan slice is then given anx-coordinate and a y-coordinate using a reference point 122 within theparticular CT scan slice that is axially aligned with point of origin116 along the z-axis.

The x, y, z coordinate for each voxel in the unified coordinate systemmay be determined as follows:

Given the following inputs:

-   -   n=CT scan slice number;    -   s=CT scan slice interval in mm (i.e., z distance between        slices);    -   x=X coordinate in mm of a point on a specific CT slice;    -   y=Y coordinate in mm of a point on a specific CT slice;    -   n_(c), x_(c), y_(c)=coordinates for the point of origin 116; and    -   n_(p), x_(p), y_(p)=coordinates of a pixel in a CT scan,        the CPU 104 assigns coordinates (X_(up), Y_(up), Z_(up)), in mm,        for each voxel in the unified coordinate system as follows:        X _(up) =x _(p) −x _(c);        Y _(up) =Y _(p) −Y _(c); and        Z _(up) =n _(p*s) −n _(c*s).

The CPU 104 renders the CT scan slices 120 as a 3D model, which isstored in memory 106. The coordinates for each pixel that was determinedby CPU 104 for each of the CT scan slices 120 ₁, 120 ₂ . . . 120 _(n)are associated with each corresponding voxel in the 3D model. Thecoordinates are then stored with the 3D model in memory 106 as voxelposition data.

When reviewed by a user, the GPU 110 processes the 3D model using thevoxel position data to align the 3D model with another 3D model obtainedfrom a different set of CT scan slices. More specifically, the two 3Dmodels are processed and displayed on the display 112 associated withworkstation 111, or in any other suitable fashion. Using workstation111, various 3D models may be presented and/or may be manipulated by aclinician to facilitate identification of a target, selection of asuitable pathway through the patient's airways to access the target,etc.

FIG. 3 depicts another method of aligning CT scan image data inaccordance with another embodiment of the present disclosure. Similar tothe method shown in FIG. 2, the point of origin 216 is located at themidst of the main carina. However, in FIG. 3, the XZ-plane is definedusing three anatomical points: the main carina; the right upper lobecarina; and the left upper lobe carina. The CPU uses the definedXZ-plane as a reference plane when determining the x, y, z coordinatesof each pixel in a particular CT scan slice. Specifically, thez-coordinate for each pixel is equal zd*cos α, where zd is the distancealong a line perpendicular to the XY-plane between the CT scan slicethat includes the point of origin 216 and the particular CT scan slicethat includes the pixel and α is the angle at the point of origin 216between the z-axis and the line perpendicular to the XY-plane. Eachpixel within the particular CT scan slice is then given an x-coordinateand a y-coordinate using a reference point 122 within the particular CTscan slice that is: coplanar with the XZ-plane; and axially aligned withpoint of origin 216 along the z-axis. Similar to the method describedabove, the CPU 104 renders the CT scan slices as a 3D model andassociates and stores the determined coordinates for each pixel in theCT scan slices for each voxel in the 3D model as voxel position data.The GPU 110 uses the 3D model using the voxel position data to align the3D model with another 3D model obtained from a different set of CT scanslices.

FIG. 4 depicts a side by side view of two (2) 3D models. 3D model 402and 3D model 404 may be rendered from CT images taken at differenttimes. Using the methods described above, each voxel in 3D model 402 and3D model 404 would be assigned an x, y, z coordinate using the maincarina as a point of origin. As such, the two (2) 3D models 402, 404would be aligned in a unified coordinate system. Aligning the two (2) 3Dmodels permits a user to track progression of a disease or results of atreatment (e.g., shrinkage of a tumor). For instance, if a tumor orlesion is found at location x₁, y₁, z₁ on 3D model 402, a user mayeasily find that location in 3D model 404 using the same coordinates.The images of these 3D models 402, 404 are preferably synchronized sothat a user can scroll through them together, but may beun-synchronized. They may also be synchronized in the sense thatchanging views or adding views to one side of the screen results in thesame on the other side. Measurement and analytics can also be done of 3Dmodels 402, 404 and tumors, etc. Such measurements and analytics may beshown on 3D models 402, 404 and reports may be generated detailing theprogress of the tumor.

The multiple sets of CT images may be used to render multiplethree-dimensional (3D) models. Using the embodiments described above,the 3D models may be aligned in a unified coordinate system anddisplayed side by side. The 3D models are preferably synchronized sothat a user can scroll through them together, but may beun-synchronized. They may also be synchronized in the sense thatchanging views or adding views to one side of the screen results in thesame on the other side. Measurement and analytics can also be done ofthe 3D models and tumors, etc. Such measurements and analytics may beshown on the 3D models and reports may be generated detailing theprogress of the tumor.

Returning to FIG. 1, CPU 104 receives various information and transformsthe received information to generate an output. CPU 104 may include anytype of computing device, computational circuit, or any type ofprocessor or processing circuit capable of executing a series ofinstructions that are stored in a memory. The CPU 104 may includemultiple processors and/or multicore central processing units and mayinclude any type of processor, such as a microprocessor, digital signalprocessor, microcontroller, or the like. The CPU 104 may also include amemory to store data and/or algorithms to perform a series ofinstructions.

Any of the herein described methods, programs, algorithms or codes maybe converted to, or expressed in, a programming language or computerprogram. A “Programming Language” and “Computer Program” is any languageused to specify instructions to a computer, and includes (but is notlimited to) these languages and their derivatives: Assembler, Basic,Batch files, BCPL, C, C+, C++, Delphi, Fortran, Java, JavaScript,Machine code, operating system command languages, Pascal, Perl, PL1,scripting languages, Visual Basic, metalanguages which themselvesspecify programs, and all first, second, third, fourth, and fifthgeneration computer languages. Also included are database and other dataschemas, and any other metalanguages. For the purposes of thisdefinition, no distinction is made between languages which areinterpreted, compiled, or use both compiled and interpreted approaches.For the purposes of this definition, no distinction is made betweencompiled and source versions of a program. Thus, reference to a program,where the programming language could exist in more than one state (suchas source, compiled, object, or linked) is a reference to any and allsuch states. The definition also encompasses the actual instructions andthe intent of those instructions.

Any of the herein described methods, programs, algorithms or codes maybe contained on one or more machine-readable media or memory 106. Theterm “memory” may include a mechanism that provides (e.g., stores and/ortransmits) information in a form readable by a machine such a processor,computer, or a digital processing device. For example, a memory mayinclude a read only memory (ROM), random access memory (RAM), magneticdisk storage media, optical storage media, flash memory devices, or anyother volatile or non-volatile memory storage device. Code orinstructions contained thereon can be represented by carrier wavesignals, infrared signals, digital signals, and by other like signals.

NIC 108 utilizes any known communication methods for transmitting and/orreceiving data to or from one or more sources.

GPU 108 is a specialized electronic circuit designed to rapidlymanipulate and alter memory to accelerate the creation of images in aframe buffer intended for output to a display.

Further aspects of image and data generation, management, andmanipulation useable in either the planning or navigation phases of anENB procedure are more fully described in commonly-owned U.S.Provisional Patent Application Ser. No. 62/020,220 entitled “Real-TimeAutomatic Registration Feedback,” filed on Jul. 2, 2014, by Brown etal.; U.S. Provisional Patent Application Ser. No. 62/020,177 entitled“Methods for Marking Biopsy Location,” filed on Jul. 2, 2014, by Brown;U.S. Provisional Patent Application Ser. No. 62/020,240 entitled “Systemand Method for Navigating Within the Lung,” filed on Jul. 2, 2014, byBrown et al.; U.S. Provisional Patent Application Ser. No. 62/020,238entitled “Intelligent Display,” filed on Jul. 2, 2014, by Kehat et al.;U.S. Provisional Patent Application Ser. No. 62/020,245 entitled“Alignment CT,” filed on Jul. 2, 2014, by Klein et al.; U.S. ProvisionalPatent Application Ser. No. 62/020,250 entitled “Algorithm forFluoroscopic Pose Estimation,” filed on Jul. 2, 2014, by Merlet; U.S.Provisional Patent Application Ser. No. 62/020,261 entitled “System andMethod for Segmentation of Lung,” filed on Jul. 2, 2014, by Markov etal.; U.S. Provisional Patent Application Ser. No. 62/020,253 entitled“Trachea Marking,” filed on Jul. 2, 2014, by Lachmanovich et al.; U.S.Provisional Patent Application Ser. No. 62/020,257 entitled “AutomaticDetection Of Human Lung Trachea,” filed on Jul. 2, 2014, by Markov etal.; U.S. Provisional Patent Application Ser. No. 62/020,261 entitled“Lung And Pleura Segmentation,” filed on Jul. 2, 2014, by Markov et al.;U.S. Provisional Patent Application Ser. No. 62/020,258 entitled “ConeView—A Method Of Providing Distance And Orientation Feedback WhileNavigating In 3d,” filed on Jul. 2, 2014, by Lachmanovich et al.; andU.S. Provisional Patent Application Ser. No. 62/020,262 entitled“Dynamic 3D Lung Map View for Tool Navigation Inside the Lung,” filed onJul. 2, 2014, by Weingarten et al., the entire contents of all of whichare hereby incorporated by reference. Any of the herein describedsystems and methods may transfer data therebetween over a wired network,wireless network, point to point communication protocol, a DICOMcommunication protocol, a transmission line, a removable storage medium,and the like.

Although embodiments have been described in detail with reference to theaccompanying drawings for the purpose of illustration and description,it is to be understood that the inventive processes and apparatus arenot to be construed as limited thereby. It will be apparent to those ofordinary skill in the art that various modifications to the foregoingembodiments may be made without departing from the scope of thedisclosure.

What is claimed is:
 1. A computed tomography (CT) alignment systemcomprising: a memory configured to store a plurality of CT images,wherein a distance between every two adjacent CT images is the samealong a z-axis in an XYZ coordinate system; a processor configured toprocess a plurality of CT images stored in the memory by: setting aslice number for each of the plurality of CT images, wherein each pixelin each CT image has an x′-coordinate and a y′-coordinate in an X′Y′coordinate system; selecting a reference CT image, which includes a maincarina, from the plurality of CT images; setting a location of the maincarina in the reference CT image as an origin of the XYZ coordinatesystem; calculating an x-coordinate, a y-coordinate, and a z-coordinateof each pixel in each CT image in the plurality of CT images based onthe origin and slice numbers in the XYZ coordinate system; and thegenerating a 3D model from the plurality of CT images by assigning anx-coordinate, a y-coordinate, and a z-coordinate of each voxel in the 3Dmodel as voxel position data based on the x-, y-, and z-coordinates of acorresponding pixel, respectively; and a graphics processing unit (GPU)configured to render and display the 3D model on a display, wherein thex-coordinate of each pixel in each CT image in the XYZ coordinate systemis calculated by subtracting an x′-coordinate of the origin from anx′-coordinate of each pixel in each CT image in the X′Y′ coordinatesystem.
 2. The CT alignment system according to claim 1, wherein each CTimage has been captured parallel to an XY plane of the XYZ coordinatesystem.
 3. The CT alignment system according to claim 1, wherein they-coordinate of each pixel in each CT image in the XYZ coordinate systemis calculated by subtracting a y′-coordinate of the origin from ay′-coordinate of each pixel in each CT image in the X′Y′ coordinatesystem.
 4. The CT alignment system according to claim 1, wherein thez-coordinate of each pixel in each CT image in the XYZ coordinate systemis calculated:N _(p) *S−N _(c) *S, where Np is a slice number of each CT image, Nc isa slice number of the reference CT image, and S is the distance betweenevery two adjacent CT images.
 5. A computed tomography (CT) alignmentmethod comprising: setting a slice number for each of a plurality of CTimages stored in a memory, wherein a distance between every two adjacentCT images is same along a z-axis in an XYZ coordinate system, whereineach pixel in each CT image has an x′-coordinate and a y′-coordinate inan X′Y′ coordinate system; selecting a reference CT image, whichincludes a main carina, from the plurality of CT images; setting alocation of the main carina in the reference CT image as an origin ofthe XYZ coordinate system; calculating an x-coordinate, a y-coordinate,and a z-coordinate of each pixel in each CT image in the plurality of CTimages based on the origin and slice numbers in the XYZ coordinatesystem; generating a 3D model from the plurality of CT images byassigning an x-coordinate, a y-coordinate, and a z-coordinate of eachvoxel in the 3D model as voxel position data based on the x-, y-, andz-coordinates of a corresponding pixel, respectively; and rendering anddisplaying the 3D model on a display, wherein the x-coordinate of eachpixel in each CT image in the XYZ coordinate system is calculated bysubtracting an x′-coordinate of the origin from an x′-coordinate of eachpixel in each CT image in the X′Y′ coordinate system.
 6. The CTalignment method according to claim 5, wherein each CT image has beencaptured parallel to an XY plane of the XYZ coordinate system.
 7. The CTalignment method according to claim 5, wherein the y-coordinate of eachpixel in each CT image in the XYZ coordinate system is calculated bysubtracting y′ coordinate of the origin from a y′-coordinate of eachpixel in each CT image in the X′Y′ coordinate system.
 8. The CTalignment method according to claim 5, wherein the z-coordinate of eachpixel in each CT image in the XYZ coordinate system is calculated:N _(p) *S−N _(c) *S, where N_(p) is a slice number of each CT image,N_(c) is a slice number of the reference CT image, and S is the distancebetween every two adjacent CT images.
 9. A non-transitory computerreadable medium storing instructions to perform a computed tomography(CT) alignment method comprising: setting a slice number for each of aplurality of CT images stored in a memory, wherein a distance betweenevery two adjacent CT images is same along a z-axis in an XYZ coordinatesystem wherein each pixel in each CT image has an x′-coordinate and ay′-coordinate in an X′Y′ coordinate system; selecting a reference CTimage, which includes a main carina, from the plurality of CT images;setting a location of the main carina in the reference CT image as anorigin of the XYZ coordinate system; calculating an x-coordinate, ay-coordinate, and a z-coordinate of each pixel in each CT image in theplurality of CT images based on the origin and slice numbers in the XYZcoordinate system; generating a 3D model from the plurality of CT imagesby assigning an x-coordinate, a y-coordinate, and a z-coordinate of eachvoxel in the 3D model as voxel position data based on the x-, y-, andz-coordinates of a corresponding pixel, respectively; and rendering anddisplaying the 3D model on a display, wherein the x-coordinate of eachpixel in each CT image in the XYZ coordinate system is calculated bysubtracting an x′-coordinate of the origin from an x′-coordinate of eachpixel in each CT image in the X′Y′ coordinate system.
 10. Thenon-transitory computer readable medium according to claim 9, whereineach CT image has been captured parallel to an XY plane of the XYZcoordinate system.
 11. The non-transitory computer readable mediumaccording to claim 9, wherein the y-coordinate of each pixel in each CTimage in the XYZ coordinate system is calculated by subtracting ay′-coordinate of the origin from a y′-coordinate of each pixel in eachCT image in the X′Y′ coordinate system.
 12. The non-transitory computerreadable medium according to claim 9, wherein the z-coordinate of eachpixel in each CT image in the XYZ coordinate system is calculated:N _(p) *S−N _(c) *S, where N_(p) is a slice number of each CT image,N_(c) is a slice number of the reference CT image, and S is the distancebetween every two adjacent CT images.